Nowadays use of Computational Fluid Dynamics (CFD) is extended in the aeronautical industry. In order to reduce investment in Wind Tunnel Tests simulation is increasingly used in design activities.
CFD discretizes the physical domain into small cells where the Navier-Stokes equations or simplifications of them, for example the Reynolds Averaged Navier-Stokes, are computed. That implies that in order to perform a good computation one needs a good mesh. Mesh quality is usually defined by cell deformation or the growing ratio between cells. Also residuals computed in the equations give a good idea of the quality of the computation.
Hybrid turbulence modeling simulations that use a combination of Reynolds-averaged Navier-Stokes (RANS) equations and large-eddy simulation (LES) are becoming increasingly popular to increase predictive accuracy in complex flow situations (specially in detached flows) without the cost of full large-eddy simulations. Hybrid methods that use RANS and LES need to adapt the mesh for the use of both methodologies in the same computations, so that a mesh with a RANS zone relatively coarse (compared with LES zone) is needed and a zone of high resolution without propagation to the RANS zone is also a need for the LES zone. As LES demands to be non-stationary RANS is used in non-stationary mode (Unstationary RANS or URANS). LES is a turbulence modeling method with a subgrid scale model, that means that mesh resolution can have some influence on the final solution. There is no mesh convergence, there is a solution convergence as the more refinement generated the more scales are resolved. That implies that a good quality in a LES zone is defined by the mesh resolution.
The meshes mainly used in CFD are of three types: entirely structured, totally unstructured or hybrid, that is a mixture of these two mesh types.
Structured meshes are meshes whose connectivity is regular and fixed by the topology: each inner vertex is topologically connected to his neighbors inside the block. Also the number of cells are propagated inside the block and to the neighbor blocks. All nodes inside a structured mesh can be located using indexes (l,j,k), so that connectivity is explicit.
Unstructured meshes have a completely arbitrary connectivity: a vertex of the mesh can belong to non obvious cells. The topological data therefore have to be permanently stored to explicitly know the neighbors of each node. The memory cost involved by the use of an unstructured mesh can therefore become very rapidly penalizing.
For complex geometries structured meshes are divided in several blocks, creating multiblock-structured-meshes in which the actual geometry is formed by several structured blocks, having structurally ordered meshes inside them.
The location and distribution of blocks in the physical domain, i.e. the mesh topology, play a significant role for achieving a good description of the geometry. The connection between blocks is also important due to the node propagation, as block faces propagate the numbers of nodes between two blocks in contact.
On the other hand, equations can define a special physics called Boundary Layer (BL) behavior, this BL not only appears in CFD equations, also other equations can create this BL behavior and will have similar treatment. This BL behavior forces mesh topologies to create a “C” topology around the surfaces. “C” topology is defined as a topology that surrounds the airfoils (and the objects inside the flow) so that mesh refinement is not propagated upstream the airfoil and only located downstream. FIG. 1 shows an example of a “C” topology around an 2D airfoil. In hybrid methods (RANS/LES) the boundary layer zone must be described using RANS.
Several constrains are usually applied to mesh topology definitions, such as the following:                The need that the topology must mark the limits of the surfaces.        The need that the topology must take into account the geometrical discontinuities of the surfaces.        The need to use a “C” topology around the surfaces caused by a Boundary Layer (BL) behavior.        
A typical mesh quality requirement is that the cells are as close as possible to perfect cubes (3D) or squares (2D). In order to check that quality requirement there are several mathematical formulas, for example, assuring that no one of the planar angles is below 20-30°, also another criteria could be the angle formed by whatever diagonals of the cubes (or the squares) not lower to 20-30° too, or the determinant of the transformation is up to 0.2. For LES computations also one must assure that the refinement is good enough for have a good description of eddies.
All structured meshes have their blocks topologically connected at the interfaces, that means that interfaces must have exactly the same number of nodes (continuity). There is a possibility of creating TNC (total-non-coincident) nodes interfaces where a jump in the number of cells and distribution can be found. Their use can create problems in interpolations, however reduces the number of nodes. A good strategy is to use TNCs at low gradient zones, this zones are usually called “euler” zones as they are zone far from the wall boundaries and their flux is close to an euler flux. Generally is recommended to avoid TNC inside boundary layers.
Although hybrid methods have not been widely use in industry, some applications for airfoils have been disclosed.
The use of a traditional “C” topology is disclosed in “Detached-Eddy Simulation of Three Airfoils with Different Stall Onset Mechanisms”. Dong Li, Igor Men'shov and Yoshiaki Nakamura. Journal of Aircraft Vol 43 No. 4. July-August 2006.
The use of an “O” topology is disclosed in “Detached-Eddy Simulation for Iced Airfoils”. Jianping Pan and Eric Loth. Journal of Aircraft Vol 42 No. 6 November-December 2005.
The use of new topologies is disclosed in “Detached Eddy Simulations of an Iced-Airfoil”. S. Kumar and E. Loth. 39th AIAA Aerospace Sciences Meeting and Exhibit. 8-11 Jan. 2001. Reno.
The increasing use of hybrid method demands optimized CFD models and the present invention is intended to attend this demand.